Answered

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PARTAPoints A, B, and C are collinear. Point B is the midpoint of AC AB = 2x + 16 and BC = 4x - 4. Find AC.

Sagot :

Points A, B, and C are collinear, then:

AB + BC = AC

Point B is the midpoint of AC, then:

AB = BC

Replacing with the equations of AB and BC, we get:

2x + 16 = 4x - 4

2x is adding on the left, then it will subtract on the right

4 is subtracting on the right, then it will add on the left

16 + 4 = 4x - 2x

20 = 2x

2 is multiplying on the right, then it will divide on the left

20/2 = x

10 = x

Then:

AB = 2x + 16 = 2(10) + 16 = 20 + 16 = 36

BC = 4x - 4 = 4(10) - 4 = 40 - 4 = 36

AC = AB + BC = 36 + 36 = 72

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